Stability of multivalued attractor

Miroslav Rypka



Stimulated by recent problems in the theory of iterated function systems, we provide a variant of the Banach converse theorem for multivalued maps. In particular, we show that attractors of continuous multivalued maps on metric spaces are stable. Moreover, such attractors in locally compact, complete metric spaces may be obtained by means of the Banach theorem in the hyperspace.


Converse of Banach theorem; multivalued map; multivalued attractor; stability

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